Multiple search direction conjugate gradient method I: methods and their propositions

Authors: Tongxiang Gu¹; Xingping Liu²; Zeyao Mo²; Xuebin Chi¹

Source: International Journal of Computer Mathematics, Volume 81, Number 9, September 2004 , pp. 1133-1143(11)

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Abstract:

In this article, we proposed a new CG-type method based on domain decomposition method, which is called multiple search direction conjugate gradient (MSD-CG) method. In each iteration, it uses a search direction in each subdomain. Instead of making all search directions conjugate to each other, as in the block CG method [O'Leary, D. P. (1980). The block conjugate gradient algorithm and related methods. Lin. Alg. Appl., 29, 293-322.], we require that they are nonzero in corresponding subdomains only. The GIPF-CG method, an approximate version of the MSD-CG method, only requires communication between neighboring subdomains and eliminate global inner product entirely. This method is therefore well suited for massively parallel computation. We give some propositions and a preconditioned version of the MSD-CG method.

Keywords: Linear systems; Conjugate gradient-type method; Massively parallel computing; Inner product; Global communication

Document Type: Research article

DOI: http://dx.doi.org/10.1080/00207160410001712305

Affiliations: 1: Supercomputing Center of Computer Network Information Center Chinese Academy of Science P.O. Box 349 Beijing 100080 P.R. China 2: Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing 100088 P.R. China

Publication date: 2004-09-01

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